Contents Online
Acta Mathematica
Volume 219 (2017)
Number 1
Singular Ricci flows I
Pages: 65 – 134
DOI: https://dx.doi.org/10.4310/ACTA.2017.v219.n1.a4
Authors
Abstract
We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. These provide a solution to the long-standing problem of finding a good notion of Ricci flow through singularities, in the $3$-dimensional case.
We prove that Ricci flow with surgery, starting from a fixed initial condition, subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.
Research supported by NSF grants DMS-1105656, DMS-1207654 and DMS-1405899, and a Simons Fellowship.
Received 16 November 2015
Accepted 28 October 2017
Published 31 January 2018